A new nonlinear fracture analysis framework is developed for the mode-I and II fracture response of thick-section fiber reinforced polymeric (FRP) composites. This framework employs 3D micromechanical constitutive models for the nonlinear material behavior along with cohesive elements for crack growth. Fracture tests on various cracked geometries are used to verify the prediction of the failure loads and the crack growth behavior. A commercially available pultruded E-glass/polyester and vinylester thick-section FRP composite material was used to demonstrate the proposed fracture approach along with the nonlinear constitutive modeling. A new Infra-red thermography technique is derived to measure the surface strain field near the crack tip in the linear response range. Mode I and II fracture toughness tests for pultruded composites are also examined using the eccentrically loaded, single-edge-notch tension, ESE(T), single-edge-notch tension, SEN(T), and a butterfly specimen with an Arcan-type fixture. Material nonlinearity and crack growth effects were observed during the tests and investigated using the proposed analysis framework. The effect of material orthotropy on the stress intensity factor solutions was addressed using the virtual crack closure technique. The analytic and experimental results support the use of the ESE(T) specimen for the measuring the mode-I fracture toughness and the butterfly shaped specimen for measuring the mode-II toughness. The calibrated cohesive models were able to predict the measured crack growth in both modes I and II for various crack geometries. A mixed mode failure criterion is proposed and verified with test results. Examples are presented for using this criterion and crack growth analyses. The experimental and analytical results of this study can form a foundation for using fracture-based methods for the design of structures using these materials.